They are the second group of a planned transfer of up to 200 youngsters stuck in the camp who have been identified by the Red Cross as eligible to go to Britain.
The new arrivals follow an advance party of five children -- four Syrians and one Afghan, who arrived in the UK at the weekend. The children were taken to a government center in south London for registration before being united with their families.
"These vulnerable children, aged between 14 and 17, were transferred to the UK under the care of Home Office staff, with the support of volunteers from specialist NGOs and charities," the UK Home Office said in a statement. "They will join their families in the UK as quickly as possible over the coming days."
Earlier, the UK government said it had sent a team to France to help identify those children eligible to come to Britain following a meeting between the UK Home Secretary Amber Rudd and her French counterpart Bernard Cazeneuve.
All the children admitted so far qualify for relocation under European Union common asylum rules.
The UK Home Office added: "When she [Amber Rudd] met the French Interior Minister this week she made it crystal clear that we intend to transfer as many minors as possible, who qualify for transfer to the UK to claim asylum on the basis of close family in the UK under the Dublin Regulation, before the start of the clearance."
"In addition, children who are eligible to come to the UK under the Dubs Amendment to the Immigration Act 2016 must be looked after in safe facilities where their best interests are properly considered. Lord Dubs was himself a child refugee who came to the UK to escape Nazi Germany. Work is continuing on both sides of the Channel to ensure this happens as a matter of urgency."
In March, the UK's upper legislative body, the House of Lords, voted against the government and backed an amendment to the 2016 Immigration Act by the Labour peer Lord Dubs to allow 3,000 unaccompanied child refugees into the country.
In total, more than 140 unaccompanied children have been accepted for transfer under Dublin family reunification so far this year (up to October 1), with more than 80 from France.
The squalid and overcrowded camp in Calais is home to 10,000 people who, having entered Europe, are trying to get across the Channel to the UK.
It is due to be demolished by French authorities later this month.
"As the camp's closure looms, I am relieved that the first children are starting to come to the UK under fast track arrangements, and can now start recovering from their ordeals," said Anne Longfied, the Children's Commissioner for England.
"Apart from those with rights to come to the UK there are several hundred other children in the camp, the vast majority on their own."
Some estimates put the number of unaccompanied children in the Calais camp at 900, just a proportion of the tens of thousands believed to be in Europe, alone and vulnerable, as Europe's refugee crisis shows no sign of abating.